Perturbation theory is the standard method to study quantum field theories in the small coupling regime. However, the interplay of the perturbative expansion and the thermodynamic limit remains controversial. In particular, arguments were put forward that the infinite volume limit of perturbative coefficients does not give the correct infinite volume asymptotic perturbation expansion of asympto...

Stresses around two parallel cracks of equal length in an infinite elastic medium are evaluated based on the linearized couple-stress theory under uniform tension normal to the cracks. Fourier transformations are used to reduce the boundary conditions with respect to the upper crack to dual integral equations. In order to solve these equations, the differences in the displacements and in the ro...

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one can not go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the contro...

We consider steady state temperature distribution in a homogeneous rectangular infinite plate the lower part of which is cooled by a fluid flowing at a constant velocity while the upper part satisfies the general mixed boundary conditions. The Wiener-Hopf method has been used to obtain the solution in the infinite series form and some special cases have been discussed.

We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of minimizers on flat two-tori, depending on the areas to be enclosed.

The dock problem (cf. [2], [4, 5]), which is that of understanding the scattering of surface water waves by a thin semi-infinite rigid plate floating on the free surface of water of infinite depth, gives rise to the following mixed boundary value problem, involving Laplace’s equation in two dimensions, with (x, y) representing the rectangular Cartesian coordinates, assuming linearised theory of...

in this work, the mechanism for fracture of brittle substances such as rocks under a uniform normal tension is considered. the oriented straight micro-cracks are mostly created in all the polycrystalline materials resulting from the stress concentrations. the present work focuses on the interactions of the pre-existing micro-cracks, which can grow and propagate within a rock-like specimen. the ...

Given a TQFT in dimension d + 1, and an infinite cyclic covering of a closed (d + 1)-dimensional manifold M , we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams’ work in symbolic dynamics. The Turaev-Viro module associated to a TQFT and an infinite cyclic covering is then given by the Jordan form...